1. Introduction

Emerging radio frequency (RF) wireless communication utilizes dynamic usage of spectrum to fulfill the needs in heterogeneous and multiband communication applications [1,2]. Due to the ever-increasing operation bandwidth of modern RF systems, the ubiquitousness of high capacity and always-on mobile devices as well as the data-intensive day-to-day applications, there is a critical need of adaptive RF spectral shaping systems, such that new applications can be supported and quality of services can be guaranteed in dynamic multi-function RF applications [3–5]. For decades, tunable and reconfigurable bandpass and notch filters are the major devices for spectral processing and noise removal. Nevertheless, it is challenging to dynamically process and manipulate a wide RF spectrum that spans across tens of GHz bandwidth using either RF electronics or digital signal processing. The challenge is due to the limited wideband functionality of RF electronics as well as the large amount of sampling and computation power needed in digital signal processing. Although electronic-based RF spectral shaping provides on-chip solutions [6], the tight design criteria and inherent inflexibility in electronics limit the operation bandwidth, the variety of the spectral shaping function, as well as tunability and reconfigurability of the spectral functions that could be achieved [7,8].

Microwave photonics has been a good candidate to tackle various challenges of its electronic counterpart due to its merits of large operation bandwidth, high tunability, and high reconfigurability [9,10]. Extensive efforts have been made to spectrally processing RF signal using photonics in various ways, including spectral shaping [11,12], single and multiband spectral filtering [13], spectral channelizing [14,15], and spectrum analyzing [16]. A lot of successes have been achieved in the field of microwave photonic filtering [17,18] over the last decade, that provides single passband or multiband filtering with mainly Gaussian profile. Passband filtering can be regarded as one type of spectral shaping and is deemed to be the nature way for implementing RF spectral shaping. However, it is challenging to achieve RF spectral shaping with good spectral resolution, multiple independent spectral control points, complex shaping functions, and high reconfigurability over tens of GHz frequency range. For example, single passband/notch filter cannot be used to control complex RF function spanning across tens of GHz RF spectrum. Recent research focus on shrinking the bandwidth of passband/notch to increase the resolution of a RF control point [19,20]; however, the fine RF control point cannot be scaled up for processing RF spectrum that span across tens of GHz range. Cascaded configuration could potentially provide multiple control points [21] but the resultant system could be expensive and have high power consumption.

Several potential candidates for wideband RF spectral shaping have been proposed including multi-pump Brillouin based microwave photonic filter [12], FIR based multiband microwave photonic spectral filter [22], and Kerr comb based RF bandwidth scaling [23]. However, each technique faces critical challenges on implementing RF spectral shaper with complex and adaptive functions. For example, Brillouin technique provides a resolution as high as 32 MHz but lacking spectral profile reconfigurability due to the difficulties in independent gain profile control with multiple Brillouin pumps [12]. Direct FIR based spectral shaping approach [24] have one major limitation is that complex and precise phase manipulation of the optical spectrum is necessary to satisfy the Fourier transform relationship between the optical and RF domains. Unfortunately, it is very challenging to achieve rapid phase control beyond -π to π of each comb lines in the optical comb carrier with existing technologies, resulting in distorted RF spectral response. As a result, only simple RF spectral shaping function including Gaussian, triangular, and flattop have been obtained using the direct FIR based spectral shaping approach. On the other hand, FIR microwave photonic multiband filter offers wideband RF spectral shaping capability, but most existing approaches shows a tight spectral relation between each passband, limiting its independent control capability. To fulfill the requirements in dynamic and wideband RF communication systems, there is a critical need for multi-point dynamic spectral control over a wide bandwidth with varying resolution.

In this letter, a novel adaptive microwave photonic RF spectral shaper with multiple adaptive spectral control points over wideband operation frequency range of 10 GHz is proposed and experimentally demonstrated. The proposed scheme can process the whole frequency band simultaneously with arbitrary/user-defined RF response instead of using single/multiband filter with fixed spectral shape (e.g. triangular, Gaussian, flat-top, etc.). To overcome the phase limitation in direct FIR scheme, this proposed approach automatically breaks down the target spectral response into a unique series of Gaussian functions according to its spectral characteristic, such that manipulation of optical phase is not required. Then the corresponding sets of finite impulse responses (FIR) parameters are simultaneously generated. The FIR parameters are combined and is then used to control the generation of interleaving optical comb carrier with the correct weight and delay, as illustrated in Fig. 1. In this way, the target spectral response can be reconstructed from the shaped optical comb carrier after photodetection. Unlike optical to RF spectral mapping approach where the RF resolution is fixed and directly limited by the optical spectral resolution, our scheme is based on the use of multiple FIR to generate the interleaved optical comb carriers with all the needed free spectral range (FSR) for the reconstruction of the target RF spectral function, which significantly improved the step resolution to less than 10 MHz. Therefore, the proposed scheme enables adaptive RF spectral shaping with flexible spectral profile through the automatic spectral decomposition and reconstruction processes.

 

Fig. 1. Adaptive photonic RF spectral shaper with automatic control algorithm.

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2. Experimental details

Figure 2 shows the experimental setup of the proposed RF spectral shaper. A superluminescent diode (Thorlabs SLD S5FC1005S) is used as a broadband optical source, which covers the wavelength range from 1528 nm to 1568 nm. An optical wave shaper (Finisar 1000S) is used for controlling the optical spectral properties of the broadband optical source through spectral slicing, such that interleaved combs with the designed amplitude, bandwidth, spacing, and envelope profile can be generated all at once based on the results from the RF spectral decomposition algorithm. Since optical comb generation and comb profile shaping are performed at the same time at the optical waves shaper, no complex spectral alignment or calibration is needed [25,26]. A 12-GHz electro-optic modulator (Fujitsu FTM7921ER) is used to modulate the RF signal from the remote RF core onto the shaped comb carrier. In our experiment, a sweeping RF signal from a 20-GHz vector network analyzer (Agilent E5071C) is used as the RF input for characterizing the proposed RF spectral shaper. The FIR tap delay is provided by the dispersion compensating fiber (DCF) with length of 2.5 km and group velocity dispersion of 170 ps/nm/km. An 18-GHz photodetector is used to convert the modulated optical comb carrier back to RF domain and the resultant RF response is measured by the VNA. The enabler of the adaptive and independent multi-point control of the RF spectral response is the two-section algorithm for optimized decomposition and reconstruction of the target RF response.

 

Fig. 2. Experimental setup of the multi-point adaptive RF spectral shaper. SLD: superluminescent diode; WS: optical wave shaper; EOM: electro-optic modulator; DCF: dispersion compensating fiber; PD: photodetector; VNA: vector network analyzer. MP: microprocessor (Red line: optical paths; dashed blue line: electrical paths; black line: computer control paths).

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2.1 RF spectral decomposition and optimization

Based on radial basis decomposition [27,28], wideband RF spectrum can be represented by orthogonal basis in the form of a series of Gaussian functions with different bandwidth and amplitude; similar to how a repetitive time domain waveform can be decomposed into a series of sinusoid basis at different frequency. Therefore, given a target RF spectral response (e.g. complementary RF response for equalization in Fig. 3(a)i), the target response can be decomposed into a series of Gaussian functions, as shown in Fig. 3(a)ii. The decomposition process is achieved by having Gaussian peaks aligning at the maxima of the RF response, while the overlapping of the tails of Gaussian functions forms the minima or plateaus. Therefore, a widely spaced subset of Gaussian functions with wide bandwidth will lead to a gentle change in the resultant RF spectral response with coarse spectral control. While fine control of sharp amplitude changes in the RF response can be achieved by offset-overlapping a narrow bandwidth Gaussian function with a main wideband Gaussian function. Furthermore, overlapping regions between each Gaussian function could constitute a valley or plateau in the RF response. Therefore, the Gaussian functions could be spaced unevenly, and the number of Gaussian functions corresponds to the number of control points needed in the RF spectrum reconstruction. On the other hand, if the direct FIR approach is used, complex and fast phase varying optical spectrum is required to reconstruct the target spectrum, as shown by the simulation results in Fig. 3(c), which is extremely difficult to achieve. The goal of the algorithm (Algorithm 1) is to identify and optimize the Gaussian functions with different amplitude and bandwidth properties needed in the target RF spectral response, including the total number of Gaussian functions n for RF spectral reconstruction and the detail parameters of the i^th Gaussian function, such as amplitude C_i, center frequency f_c-i, and 3-dB bandwidth f_3dB-i.

 

Fig. 3. Illustration of the automatic RF spectral decomposition and reconstruction process. (a)(i) received RF spectrum/response (grey); target RF response (black); equalized response (blue); (ii) optimized and decomposed spectra of Gaussian functions; (iii) reconstructed RF spectra (red) and target RF response (black) in log scale. (b) Corresponding optical spectral control with independent comb properties based on the proposed spectral decomposition scheme (I-IV: blue, orange, green and red) and corresponding aggregated optical spectrum (V: purple). (c) Simulated amplitude and phase requirement of the optical spectrum for the reconstruction of the target RF response in (a) using direct FIR approach.

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Mathematical expression of the decomposed RF response can be expressed as series of Gaussian functions as described below,

Although the discrepancy between the target RF response and the reconstructed RF response could be reduced using a large number of Gaussian functions, an overly large number of Gaussian functions will consequently degrade the optical comb carrier quality, i.e. the comb features could be masked by another comb, and negatively affect the RF response reconstruction performance. Therefore, the proposed algorithm (Algorithm 1) aims to identify the optimized number (n) of Gaussian functions needed for RF response reconstruction while keeping the discrepancy within the tolerable error limit, ε, governed by

2.2 RF spectral reconstruction

Once the RF spectral decomposition algorithm has determined all the feature parameters for the set of Gaussian functions, second part of the algorithm determines the corresponding parameters for generating the optical comb carrier that forms the Gaussian functions for the reconstruction of the target RF response, including comb amplitude A_n, 3-dB optical envelope bandwidth Δω_3dB-n, and comb FSR Δω_FSR-n of the n-th group of optical comb. The n-th comb FSR and the 3-dB bandwidth are determined by,

According to Eq. (3), the minimum bandwidth of each RF control point (i.e. RF feature) is determined by the 3-dB bandwidth of the overall optical comb and the total dispersion provided. While the maximum bandwidth of each RF control point is limited by how narrow the overall optical comb bandwidth could be as well as the photodetector bandwidth. Suppose the dispersion constant β₂ is unchanged, the resultant bandwidth range of each RF control point can be from several tens of MHz to a few GHz, as depicted in Fig. 4(a).

 

Fig. 4. Simulation results of (a) Bandwidth of each RF control point (i.e. RF feature) vs 3-dB optical bandwidth and length of DCF, with fixed dispersion constant; (b) Step resolution of each RF control point vs comb spacing and length of DCF, with fixed optical waveshaper step (i.e. addressability); (c) Step resolution of each RF control point vs comb spacing and optical waveshaper step, with fixed dispersion constant.

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In addition, the RF step resolution Δf_step, i.e. how close two RF control points can be placed, is simulated and is shown in Fig. 4(b). It is observed that the larger the optical comb spacing, the finer the RF step resolution would be. The addressability of the optical waveshaper also plays a role in governing the RF step resolution, as shown in Fig. 4(c). The optical step resolution in the optical waveshaper governs the precision of the optical comb FSR, which in turn determines the step resolution of the RF response. The mathematical relationship can be expressed as,

In our experiment, the optical waveshaper used for generating the optical comb carriers has a spectral resolution of 12 GHz, and an addressability of 1 GHz. As illustrated in Fig. 5(a), the user can control the amplitude of each 1-GHz point (red shaded area in the left cycle), while each 1-GHz point has a 12-GHz full bandwidth (purple shaded area). Therefore, to construct a periodic cosine function (red dashed line in Fig. 5(a)) using the optical waveshaper, the amplitude at each 1-GHz spacing (alternate red and yellow shaded area) is set to the corresponding value of a sinusoidal function. The resultant optical comb will be of a periodic quasi-sinusoidal function due to the 12-GHz spectral resolution of the optical waveshaper (black solid line in Fig. 5(a)). However, the slight difference between periodic desired and quasi-sinusoidal shape will not distort the resultant target RF response because all the essential parameters are still accurately represented in the resultant optical combs.

 

Fig. 5. (a) Illustration of optical spectral processing for multiple control points at waveshaper; (b) Samples of simple RF responses achieved by the RF spectral shaper that are commonly needed in RF systems.

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We did a preliminary experiment to verify the RF spectral shaper’s ability to generate different RF spectral shaping/equalization functions across a 10 GHz bandwidth. Showing in Fig. 5(b) are examples of several commonly needed RF spectral response in RF systems including negative linear response with variable slopes (red and sky blue), sinusoid (orange), and flat-top/multi-peak bandpass-shaping (green and purple). The generated RF responses show dynamic, precise, and continuous spectral tailoring capability of the proposed RF spectral shaper. It is important to mention that the orthogonal Gaussian basis used in the proposed algorithm is to provide a general yet dynamic decomposition solution for complex wideband RF response. In our experiment, the narrowest bandwidth obtained by the RF Gaussian function is 180 MHz, while the widest bandwidth is expected to be 55 GHz if the modulator and the photodetector could support.

Next, we demonstrate the feasibility of adaptive spectral control for simultaneous multiband (S, C, and X bands) spectral shaping with non-uniform and fully customizable spectral properties using the proposed two-section algorithm, as shown in Fig. 6. First, the target RF response is defined by the user – indicated by the dashed red curve (in linear scale) in Fig. 6(a). The target function in log scale is shown by the dashed red curve in Fig. 6(b). The function is designed for supporting simultaneous Bluetooth/WiFi transmission (S band) as well as gain equalization at higher frequency range (C + X bands). The proposed algorithm automatically decomposed the target RF response into an optimized number of Gaussian functions (indicated by the five color-shaded areas centered at 2.4 GHz, 3.8 GHz, 5.8 GHz, 7.8 GHz, and 8.5 GHz) for obtaining the desired RF response. Then, the algorithm generates the corresponding optical parameters for the optical comb carriers according to Eq. (3) and Eq. (4). The parameters are used to control the programmable optical processer, i.e. optical waveshaper, for generating the optical comb carriers needed for the reconstruction of the target RF response. After photodetection, the target RF response is reconstructed as shown by the black curve in Fig. 6(a) in linear scale and black curve in Fig. 6(b) in log scale. It is observed that the Bluetooth/ WiFi transmission window at 2.4 GHz (region I) has a 40-dB rejection ratio, while gain compensation in Region II and III have 10 dB (purple shaded area) and 6 dB (grey shaded area) dynamic shaping range, respectively. Although there is discrepancy between the target and resultant RF responses, the discrepancy is only less than 1%, which is marked by the green shaded region.

 

Fig. 6. Experimental results of wideband adaptive RF spectral shaper with optimized decomposition and reconstruction algorithm. (a) Target RF response (dashed red curve), reconstructed RF response (solid black curve), set of Gaussian functions (shaded); (b) Target RF response for simultaneous Bluetooth/WiFi channel filtering (region I) and spectral compensation (region II and III), mismatch are showed in green shade; (c) S + X band spectral shaping and C band transmission; (d) S + C band spectral shaping and X band transmission.

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Furthermore, different target RF response is presented to the RF spectral shaper for verifying its adaptability and reconfigurability. Figure 6(c) has a target RF response that facilitates transmission in C band and dynamic gain compensation in S + X bands, while Fig. 6(d) has a target RF response that requires dynamic spectral equalization in S + C bands and signal transmission in X band. The decomposed Gaussian functions are depicted by the color-shaded areas in the linear scale inset. The resultant RF responses generated by the RF spectral shaper are shown by the black solid curve, while the discrepancies are indicated by the green shaded areas in Figs. 6(c) and (d). The results show that the proposed RF spectral shaper has successfully adapted to changes in the user defined target RF response and generated the corresponding RF response with small discrepancy.

As the number of RF spectral control point increases, some of the optical comb feature could be masked by another comb, resulting in ripples in the resultant RF response. Here, we investigate the maximum number of RF spectral control point (number of Gaussian functions for reconstruction) supported by the RF spectral shaper without degrading the resultant RF response. First, each Gaussian function are intentionally set to have a narrow 3-dB bandwidth of 180 MHz with shaping slope of 0.03 dB/MHz and are evenly spaced at 1 GHz, as shown by the black dashed lines in Figs. 7(a) and (b), so that we can clearly observe each of the Gaussian peaks without overlapping. Bandwidth of RF control points are governed by the total dispersion, a 90 MHz bandwidth can be achieved when a 5 km DCF is used. The RF spectral shaper supports 11 spectral control points, and the control points can be placed as close as tens of MHz with uneven spacing if desired, which is governed by the addressability of the optical waveshaper and the dispersion provided. As the bandwidth of the Gaussian functions increases, as shown by the color shaded Gaussian shapes, tails of the Gaussian functions overlap and forms the valleys and plateau of the RF response, as shown by the black solid curves. Figures 7(c) and (d) shows the experimental results of the fine tuning of the center position of the RF Gaussian spectral function, which indicates that the 1 GHz addressability in the optical waveshaper results in a step resolution of 7.8 MHz and 18.3 MHz in center frequency at 3 GHz and 6 GHz in both directions, respectively.

 

Fig. 7. (a)-(b) Eleven spectral control points reconstructing a target RF response with peaks, valleys, and plateaus with 180 MHz RF control point bandwidth; (c) Measured 7.8 MHz step resolution when Gaussian RF peak is centered at 3 GHz; (d) Measured 18.3 MHz step resolution when Gaussian RF peak is centered at 6 GHz.

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3. Summary

In summary, an adaptive and customizable RF spectral shaper with tens of MHz step resolution is experimentally demonstrated that allows dynamic multi-point control of arbitrary RF spectral function. The proposed spectral shaper is capable of generating arbitrary RF spectral functions for wideband spectral tailoring, multipoint spectral control, and channel equalization. The two-section algorithm overcomes the phase limitation in direct FIR approaches by dynamically decomposes and optimizes the target RF response into a series of Gaussian functions. The algorithm then generates the corresponding parameters for the construction of the optical comb carriers that are used for the reconstruction of the target RF response. It is worth to notice that a flat RF spectral function could be challenging for the current decomposition algorithm to provide high-accuracy decomposition and reconstruction, triangular spectral functions could be added to the decomposition algorithm to tackle the challenge. In the experiment, simultaneous dynamic RF spectral shaping with user-defined shaping functions in S, C and X bands are successfully achieved. Furthermore, the proposed RF spectral shaper mitigates the optical coarse resolution in most optical to RF spectrum mapping schemes using discrete convolution technique. It is worth noting that although coherent FIR approach (i.e. using discrete lasers) provides better noise performance than incoherent FIR approach, we believe that the flexibility and shaping capability offered in the proposed incoherent approach could worth the tradeoff in scenerios that in need of the unique capabilities provided. While there are rooms to improve the noise performance, the use of incoherent RF filter for pulse shaping results in RF waveforms with reasonable noise performance in our previous study [22]. The proposed RF spectral shaper is a potential blackbox solution to future software defined radio (SDR) system due to its fully programmable capability and the automatic adaptive RF spectral decomposition and reconstruction processes.